I see a starship as more of a mobile base for your fleet, it would have abilities to repair nearby ally ships and allow your ships to escape a losing battle with fewer losses. In itself it would not be a heavy combat ship, but with massive shield and health reserves, so it wouldn't be a pushover. Maybe planet bombardment weapons, maybe colonization abilities, but slow. Slow enough to not make it a viable pursuit vessel.
A starship of this size would basically be the flagship of your whole empire, and your defense against the enemy's starship. Maybe have it so you cannot lose the game until that ship is destroyed as well as your planets. It has to be customizable, like a starbase. And also expensive so it wouldnt be possible to spam them.
For the vasari startship, it could be a mobile phase gate, allowing the fleet to jump to it from any grav well, even those without phase stabilizers. This would allow two things, either a retreat from an overwhelming enemy force, or have your starship jump to an enemy world and bring you entire fleet in behind it from any grav well.
Advent, culture bonus and strikecraft bonus. The weird advent abilities that wor so great together.
Tec, credit production. repair station. Antimatter bonus. More firepower than the other starships.
Just my two cents